Data depth-based nonparametric scale tests
Bibliographic record
Abstract
Liu and Singh (1993, 2006) introduced a depth-based d-variate extension of the nonparametric two sample scale test of Siegel and Tukey (1960). Liu and Singh (2006) generalized this depth-based test for scale homogeneity of k ≥ 2 multivariate populations. Motivated by the work of Gastwirth (1965), we propose k sample percentile modifications of Liu and Singh's proposals. The test statistic is shown to be asymptotically normal when k = 2, and compares favorably with Liu and Singh (2006) if the underlying distributions are either symmetric with light tails or asymmetric. In the case of skewed distributions considered in this paper the power of the proposed tests can attain twice the power of the Liu-Singh test for d ≥ 1. Finally, in the k-sample case, it is shown that the asymptotic distribution of the proposed percentile modified Kruskal-Wallis type test is χ2 with k − 1 degrees of freedom. Power properties of this k-sample test are similar to those for the proposed two sample one. The Canadian Journal of Statistics 39: 356–369; 2011 © 2011 Statistical Society of Canada
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.010 | 0.086 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".